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0, 0, 0, 2, 2, 4, 4, 7, 9, 11, 11, 14, 14, 16, 18, 22, 22, 25, 25, 28, 30, 32, 32, 36, 38, 40, 43, 46, 46, 49, 49, 54, 56, 58, 60, 64, 64, 66, 68, 72, 72, 75, 75, 78, 81, 83, 83, 88, 90, 93, 95, 98, 98, 102, 104, 108, 110, 112, 112, 116, 116, 118, 121, 127, 129, 132, 132
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OFFSET
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1,4
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COMMENTS
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Excess of prime-power exponents in n!.
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LINKS
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FORMULA
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EXAMPLE
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n=46: prime powers in factorization of 46! are {42,21,10,6,4,3,2,2,2,1,1,1,1,1}. Sum of the exponents is 97. It has 14 distinct prime divisors, so a(46)=97-14=83.
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MATHEMATICA
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Table[PrimeOmega[n!] - PrimeNu[n!], {n, 1, 100}] (* G. C. Greubel, May 13 2017 *)
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PROG
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(PARI) for(n=1, 100, print1(bigomega(n!) - omega(n!), ", ")) \\ G. C. Greubel, May 13 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Simpler definition from Alan Worley (aw(AT)xiboo.co.uk), Dec 10 2008
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STATUS
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approved
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